Problem: Solve for $x$ and $y$ using elimination. ${-5x-y = -48}$ ${-6x-3y = -63}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-3$ ${15x+3y = 144}$ $-6x-3y = -63$ Add the top and bottom equations together. $9x = 81$ $\dfrac{9x}{{9}} = \dfrac{81}{{9}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-5x-y = -48}\thinspace$ to find $y$ ${-5}{(9)}{ - y = -48}$ $-45-y = -48$ $-45{+45} - y = -48{+45}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 9}$ into $\thinspace {-6x-3y = -63}\thinspace$ and get the same answer for $y$ : ${-6}{(9)}{ - 3y = -63}$ ${y = 3}$